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dc.contributor.authorAdamo, Maria Stella
dc.contributor.authorNeeb, Karl-Hermann
dc.contributor.authorSchober, Jonas
dc.date.accessioned2021-12-15T07:46:41Z
dc.date.available2021-12-15T07:46:41Z
dc.date.issued2021-12-15
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3906
dc.description.abstractWe analyze reflection positive representations in terms of positive Hankel operators. This is motivated by the fact that positive Hankel operators are described in terms of their Carleson measures, whereas the compatibility condition between representations and reflection positive Hilbert spaces is quite intricate. This leads us to the concept of a Hankel positive representation of triples $(G,S,\tau)$, where $G$ is a group, $\tau$ an involutive automorphism of $G$ and $S \subseteq G$ a subsemigroup with $\tau(S) = S^{-1}$. For the triples $(\mathbb Z,\mathbb N,-id_{\mathbb Z})$, corresponding to reflection positive operators, and $(\mathbb R,\mathbb R_+,-id_{\mathbb R})$, corresponding to reflection positive one-parameter groups, we show that every Hankel positive representation can be made reflection positive by a slight change of the scalar product. A key method consists in using the measure $\mu_H$ on $\mathbb R_+$ defined by a positive Hankel operator $H$ on $H^2(\mathbb C_+)$ to define a Pick function whose imaginary part, restricted to the imaginary axis, provides an operator symbol for $H$.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2021-10
dc.subjectHankel operatoren_US
dc.subjectReflection positive representationen_US
dc.subjectHardy spaceen_US
dc.subjectWidom theoremen_US
dc.subjectCarleson measureen_US
dc.titleReflection Positivity and Hankel Operators- the Multiplicity Free Caseen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2021-10
local.scientificprogramOWLF 2021en_US
local.series.idOWP-2021-10en_US
local.subject.msc47en_US
dc.identifier.urnurn:nbn:de:101:1-2022011311532137430259
dc.identifier.ppn1786996367


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